Abstract
Using the Riemann-Liouville integration-differentiation operator, Djrbashyan generalized the class of Nevanlinna’s meromorphic functions in the unit circle including the product ( ) , 1 +∞ < α < − α B which in the special case of 0 = α coincide with the Blaschke product. Furthermore, when , 0 1 < α < − Djrbashyan and Zakaryan showed a connection between the products α B and B of Blaschke. In this work, we show the existence of Blaschke and Djrbashyan products with the same null sets, Taylor-Maclaurin coefficients satisfying certain new constraints. To achieve that result, we use a theorem of Shapiro and Shields and a remark from Zakaryan. We further estimate the Taylor coefficients of these functions.
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